{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:27:38Z","timestamp":1760146058839,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T00:00:00Z","timestamp":1728345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Institutional Fund Projects of Saudi Arabia","award":["IFPRC-167-130-2020"],"award-info":[{"award-number":["IFPRC-167-130-2020"]}]},{"name":"Ministry of Education","award":["IFPRC-167-130-2020"],"award-info":[{"award-number":["IFPRC-167-130-2020"]}]},{"name":"King Abdulaziz University","award":["IFPRC-167-130-2020"],"award-info":[{"award-number":["IFPRC-167-130-2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring R=Fp+w1Fp+w2Fp+w22Fp+w1w2Fp+w1w22Fp, where w12\u2212\u03b12=0, w1w2=w2w1, w23\u2212\u03b22w2=0, and \u03b1,\u03b2\u2208Fp\u2216{0}, for a prime p. We begin by introducing a Gray map defined over R, which is associated with an invertible matrix. We demonstrate its advantages over the canonical Gray map through some examples. Finally, we create new and improved quantum codes from constacyclic codes over R using Calderbank\u2013Shore\u2013Steane (CSS) construction.<\/jats:p>","DOI":"10.3390\/axioms13100697","type":"journal-article","created":{"date-parts":[[2024,10,8]],"date-time":"2024-10-08T12:02:10Z","timestamp":1728388930000},"page":"697","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Quantum Codes as an Application of Constacyclic Codes"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6799-8969","authenticated-orcid":false,"given":"Mohd Arif","family":"Raza","sequence":"first","affiliation":[{"name":"Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-2062-2548","authenticated-orcid":false,"given":"Mohammad Fareed","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"given":"Adel","family":"Alahmadi","sequence":"additional","affiliation":[{"name":"Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Widyan","family":"Basaffar","sequence":"additional","affiliation":[{"name":"Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7067-8085","authenticated-orcid":false,"given":"Manish K.","family":"Gupta","sequence":"additional","affiliation":[{"name":"Director Academics Office, Kaushalya: The Skill University, Ahmedabad 382424, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3955-7941","authenticated-orcid":false,"given":"Nadeem ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India"}]},{"given":"Abdul Nadim","family":"Khan","sequence":"additional","affiliation":[{"name":"Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1888-8154","authenticated-orcid":false,"given":"Hatoon","family":"Shoaib","sequence":"additional","affiliation":[{"name":"Research Group of Algebraic Structures and Applications, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4078-8301","authenticated-orcid":false,"given":"Patrick","family":"Sole","sequence":"additional","affiliation":[{"name":"I2M, (CNRS, Aix-Marseille University, Centrale Marseille), 163 Avenue de Luminy, 13009 Marseilles, France"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,8]]},"reference":[{"key":"ref_1","unstructured":"Nielsen, M.A., and Chuang, I.L. 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